Clean up the Simple-8b encoder code.

Coverity complained that simple8b_encode() might read beyond the end of
the 'diffs' array, in the loop to encode the integers. That was a false
positive, because we never get into the loop in modes 0 or 1, and the
array is large enough for all the other modes. But I admit it's very
subtle, so it's not surprising that Coverity didn't see it, and it's not
very obvious to humans either. Refactor it, so that the second loop
re-computes the differences, instead of carrying them over from the first
loop in the 'diffs' array. This way, the 'diffs' array is not needed
anymore. It makes no measurable difference in performance, and seems more
straightforward this way.

Also, improve the comments in simple8b_encode(): fix the comment about its
return value that was flat-out wrong, and explain the condition when it
returns EMPTY_CODEWORD better.

In the passing, move the 'selector' from the codeword's low bits to the
high bits. It doesn't matter much, but looking at the original paper, and
googling around for other Simple-8b implementations, that's how it's
usually done.

Per Coverity, and Tom Lane's report off-list.

src/backend/lib/integerset.c

@@ -773,7 +773,7 @@ intset_binsrch_leaf(uint64 item, leaf_item *arr, int arr_elems, bool nextkey)
  *
  * Simple-8b algorithm packs between 1 and 240 integers into 64-bit words,
  * called "codewords".  The number of integers packed into a single codeword
- * depends on the integers being packed: small integers are encoded using
+ * depends on the integers being packed; small integers are encoded using
  * fewer bits than large integers.  A single codeword can store a single
  * 60-bit integer, or two 30-bit integers, for example.
  *
@@ -783,11 +783,11 @@ intset_binsrch_leaf(uint64 item, leaf_item *arr, int arr_elems, bool nextkey)
  * of the absolute values.
  *
  * In Simple-8b, each codeword consists of a 4-bit selector, which indicates
- * how many integers are encoded in the codeword, and the encoded integers
+ * how many integers are encoded in the codeword, and the encoded integers are
  * packed into the remaining 60 bits.  The selector allows for 16 different
- * ways of using the remaining 60 bits, "modes".  The number of integers
- * packed into a single codeword is listed in the simple8b_modes table below.
- * For example, consider the following codeword:
+ * ways of using the remaining 60 bits, called "modes".  The number of integers
+ * packed into a single codeword in each mode is listed in the simple8b_modes
+ * table below.  For example, consider the following codeword:
  *
  *      20-bit integer       20-bit integer       20-bit integer
  * 1101 00000000000000010010 01111010000100100000 00000000000000010100
@@ -835,6 +835,7 @@ static const struct
 	{20, 3},					/* mode 13: three 20-bit integers */
 	{30, 2},					/* mode 14: two 30-bit integers */
 	{60, 1},					/* mode 15: one 60-bit integer */
+
 	{0, 0}						/* sentinel value */
 };
 
@@ -842,15 +843,20 @@ static const struct
  * EMPTY_CODEWORD is a special value, used to indicate "no values".
  * It is used if the next value is too large to be encoded with Simple-8b.
  *
- * This value looks like a 0-mode codeword,  but we check for it
+ * This value looks like a 0-mode codeword, but we check for it
  * specifically.  (In a real 0-mode codeword, all the unused bits are zero.)
  */
-#define EMPTY_CODEWORD		UINT64CONST(0xFFFFFFFFFFFFFFF0)
+#define EMPTY_CODEWORD		UINT64CONST(0x0FFFFFFFFFFFFFFF)
 
 /*
  * Encode a number of integers into a Simple-8b codeword.
  *
- * Returns the number of integers that were encoded.
+ * The input array must contain at least SIMPLE8B_MAX_VALUES_PER_CODEWORD
+ * elements.
+ *
+ * Returns the encoded codeword, and sets *num_encoded to the number
+ * input integers that were encoded.  It can be zero, if the first input is
+ * too large to be encoded.
  */
 static uint64
 simple8b_encode(uint64 *ints, int *num_encoded, uint64 base)
@@ -861,7 +867,6 @@ simple8b_encode(uint64 *ints, int *num_encoded, uint64 base)
 	uint64		diff;
 	uint64		last_val;
 	uint64		codeword;
-	uint64		diffs[60];
 	int			i;
 
 	Assert(ints[0] > base);
@@ -891,13 +896,12 @@ simple8b_encode(uint64 *ints, int *num_encoded, uint64 base)
 			selector++;
 			nints = simple8b_modes[selector].num_ints;
 			bits = simple8b_modes[selector].bits_per_int;
+
 			if (i >= nints)
 				break;
 		}
 		else
 		{
-			if (i < 60)
-				diffs[i] = diff;
 			i++;
 			if (i >= nints)
 				break;
@@ -910,7 +914,13 @@ simple8b_encode(uint64 *ints, int *num_encoded, uint64 base)
 
 	if (nints == 0)
 	{
-		/* The next value is too large and be encoded with Simple-8b */
+		/*
+		 * The first value is too large to be encoded with Simple-8b.
+		 *
+		 * If there is at least one not-too-large integer in the input, we
+		 * will encode it using mode 15 (or a more compact mode).  Hence, we
+		 * only get here, if the *first* input integer is >= 2^60.
+		 */
 		Assert(i == 0);
 		*num_encoded = 0;
 		return EMPTY_CODEWORD;
@@ -924,16 +934,18 @@ simple8b_encode(uint64 *ints, int *num_encoded, uint64 base)
 	codeword = 0;
 	if (bits > 0)
 	{
-		for (i = nints - 1; i >= 0; i--)
+		for (i = nints - 1; i > 0; i--)
 		{
+			diff = ints[i] - ints[i - 1] - 1;
+			codeword |= diff;
 			codeword <<= bits;
-			codeword |= diffs[i];
 		}
+		diff = ints[0] - base - 1;
+		codeword |= diff;
 	}
 
 	/* add selector to the codeword, and return */
-	codeword <<= 4;
-	codeword |= selector;
+	codeword |= (uint64) selector << 60;
 
 	*num_encoded = nints;
 	return codeword;
@@ -945,7 +957,7 @@ simple8b_encode(uint64 *ints, int *num_encoded, uint64 base)
 static int
 simple8b_decode(uint64 codeword, uint64 *decoded, uint64 base)
 {
-	int			selector = codeword & 0x0f;
+	int			selector = (codeword >> 60);
 	int			nints = simple8b_modes[selector].num_ints;
 	uint64		bits = simple8b_modes[selector].bits_per_int;
 	uint64		mask = (UINT64CONST(1) << bits) - 1;
@@ -954,8 +966,6 @@ simple8b_decode(uint64 codeword, uint64 *decoded, uint64 base)
 	if (codeword == EMPTY_CODEWORD)
 		return 0;
 
-	codeword >>= 4;				/* shift out the selector */
-
 	prev_value = base;
 	for (int i = 0; i < nints; i++)
 	{
@@ -976,15 +986,13 @@ simple8b_decode(uint64 codeword, uint64 *decoded, uint64 base)
 static bool
 simple8b_contains(uint64 codeword, uint64 key, uint64 base)
 {
-	int			selector = codeword & 0x0f;
+	int			selector = (codeword >> 60);
 	int			nints = simple8b_modes[selector].num_ints;
 	int			bits = simple8b_modes[selector].bits_per_int;
 
 	if (codeword == EMPTY_CODEWORD)
 		return false;
 
-	codeword >>= 4;				/* shift out the selector */
-
 	if (bits == 0)
 	{
 		/* Special handling for 0-bit cases. */

src/test/modules/test_integerset/test_integerset.c

@@ -539,6 +539,7 @@ test_huge_distances(void)
 	val = 0;
 	values[num_values++] = val;
 
+	/* Test differences on both sides of the 2^60 boundary. */
 	val += UINT64CONST(1152921504606846976) - 1;	/* 2^60 - 1 */
 	values[num_values++] = val;
 
@@ -563,16 +564,19 @@ test_huge_distances(void)
 	val += UINT64CONST(1152921504606846976) + 1;	/* 2^60 + 1 */
 	values[num_values++] = val;
 
-	val += UINT64CONST(1152921504606846976);	/* 2^60 */
+	val += UINT64CONST(1152921504606846976) + 2;	/* 2^60 + 2 */
 	values[num_values++] = val;
 
-	/* we're now very close to 2^64, so can't add large values anymore */
+	val += UINT64CONST(1152921504606846976) + 2;	/* 2^60 + 2 */
+	values[num_values++] = val;
 
-	intset = intset_create();
+	val += UINT64CONST(1152921504606846976);	/* 2^60 */
+	values[num_values++] = val;
 
 	/*
-	 * Add many more values to the end, to make sure that all the above values
-	 * get flushed and packed into the tree structure.
+	 * We're now very close to 2^64, so can't add large values anymore.  But
+	 * add more smaller values to the end, to make sure that all the above
+	 * values get flushed and packed into the tree structure.
 	 */
 	while (num_values < 1000)
 	{
@@ -580,7 +584,8 @@ test_huge_distances(void)
 		values[num_values++] = val;
 	}
 
-	/* Add these numbers to the set */
+	/* Create an IntegerSet using these values */
+	intset = intset_create();
 	for (int i = 0; i < num_values; i++)
 		intset_add_member(intset, values[i]);